Non-Aristotelian logic
Non-classical logics (and sometimes alternative logics) is the name given to formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.
Philosophical logic, especially in theoretical computer science, is understood to encompass and focus on non-classical logics, although the term has other meanings as well.
There are many kinds of non-classical logic, which include:
In Deviant Logic (1974) Susan Haack divided non-classical logics into deviant, quasi-deviant, and extended logics. The proposed classification is non-exclusive; a logic may be both a deviation and an extension of classical logic. A few other authors have adopted the main distinction between deviation and extension in non-classical logics.John P. Burgess uses a similar classification but calls the two main classes anti-classical and extra-classical.
In an extension, new and different logical constants are added, for instance the "" in modal logic, which stands for "necessarily." In extensions of a logic,
...
Wikipedia